Kershaw recently said he’d spoken only vaguely with Darvish about potential destinations. The Dodgers are among the large-market teams endeavoring to keep their payrolls under the luxury-tax threshold.

“We don’t talk a ton about where he’s at,” Kershaw said. “Obviously, I’ve made my sales pitch. So, we’ll just see what happens. We don’t talk about what offers he’s gotten or anything like that. I don’t want to pressure him too much. But, looks good playing catch, I’ll say that.”

An All-Star in each of his four full seasons (he missed all of 2015 and part of 2016 because of Tommy John surgery), Darvish in 131 career starts is 56-42 with a 3.42 ERA. His 2017 season showed a slight decline from seasons past, both in Texas and then, after a mid-summer trade, in Los Angeles. He was, at times, the pitcher who was second – to Max Scherzer – in the 2013 AL Cy Young balloting, and then oddly vulnerable in the strike zone.

In the 2017 postseason alone, he limited the Arizona Diamondbacks and Cubs to two runs over two starts and 11 1/3 innings, then, in the World Series, amid suspicions he was tipping his pitches, twice failed to pitch out of the second inning against the Astros. In Game 7 at Dodger Stadium, he was booed from the field, having recorded five outs and allowed five runs.

In three months with the Dodgers, and at the club’s urging, Darvish attempted to adjust his mechanics and slightly alter his approach. In his final three regular-season starts, his ERA was 0.47 with 21 strikeouts and one walk. What lasts in Los Angeles, however, are the two failed World Series starts, two losses that, coupled with a dismal Game 5 start from Kershaw, doomed the Dodgers.

Six years ago, the Rangers paid more than $110 million to acquire Darvish — $60 million in salary and the rest to Darvish’s team in Japan, the Nippon Ham Fighters, for whom Darvish pitched seven seasons and established himself as the best pitcher in the Pacific League. Darvish made two postseason starts for the Rangers, one each in 2012 and 2016, and lost them both. When it appeared the Rangers would not challenge for a playoff berth, they dealt Darvish at the trade deadline for three minor leaguers, including outfielder Willie Calhoun, one of the Dodgers’ top prospects.

While it has been several years since Darvish carried both the workload and raw results of a true No. 1, the long and elegant right-hander led a starter market that also included Arrieta, Lance Lynn and Alex Cobb, along with Japanese right-hander Shohei Ohtani, who is advertised as a two-way player. Ohtani signed with the Angels in the second week of December. In 2017, Darvish did make 31 starts and throw 186 2/3 innings, his highest totals since 2013. Among major league pitchers with at least 180 innings, he ranked 14th in ERA, ninth in WHIP, eighth in strikeouts per nine and 12th in strikeouts per walk.

David Price (seven years, $217 million with the Boston Red Sox), Kershaw (seven years, $215 million with the Dodgers), Scherzer (seven years, $210 million with the Washington Nationals) and Zack Greinke (six years, $206.5 million with the Arizona Diamondbacks) are the highest-paid pitchers.

Arrieta, Lynn and Cobb would appear to be the next free-agent options for clubs seeking to complete their rotations.